Theorems · Theorem · category theory

CategoryTheory.Limits.Multifork.IsLimit.fac

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MulticospanShape}
  {I : CategoryTheory.Limits.MulticospanIndex J C} {K : CategoryTheory.Limits.Multifork I}
  (hK : CategoryTheory.Limits.IsLimit K) {T : C} (k : (a : J.L) → T ⟶ I.left a)
  (hk :
    ∀ (b : J.R),
      CategoryTheory.CategoryStruct.comp (k (J.fst b)) (I.fst b) =
        CategoryTheory.CategoryStruct.comp (k (J.snd b)) (I.snd b))
  (a : J.L), CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Multifork.IsLimit.lift hK k hk) (K.ι a) = k a

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer

Cited by

5 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category